The wavefunction of a system consisting of 2n fermions has been written as a linear combination of products of n pair functions in such a way that antisymmetrisation of the total wavefunction is ensured. Proper orthonormalisation conditions necessary for a finite system have been introduced. The self-consistent field integrodifferential coupled equations for the n pair functions have then been derived from a variational principle by minimising the total energy of the system with the auxiliary orthonormality conditions. These equations are the Hartree-Fock analogues for the n pair functions in a finite system of 2n fermions. The calculated energy is clearly an upper bound to the exact energy. The relation between the total energy and the eigenvalues of the pair equation is derived. The total energy is not the sum of the pair eigenvalues. The generalisation to three, four and higher clusters is indicated.